Question

An inventor claims to have developed a heat

engine that receives 700 kJ of heat from a source

at 500 K and produces 300 kJ of net work while

rejecting the waste heat to a sink at 290 K. Is this

a reasonable claim? Why?

Answer 1

Solution;

The maximum heat efficiency of the engine is the Carnot efficiency;

$\eta_{Carnot}=1-\frac{T_2}{T_1}=1-\frac{290}{500}=0.42$

Since efficiency is defined as;

$\eta=\frac{work}{Heat}$

$0.42=\frac{W}{700}$

$W=294kJ$

Therefore it is impossible to have a work output greater than 294kJ and therefore the inventors claim is not reasonable.